energy equation for turbulent flow in a rotating system was derived in terms of second order correlation tensors, where the correlation tensors were functions of space coordinates, distance between two points and time. to reveal the relationship of turbulent energy between two points, one point was taken as origin of the coordinate system. due to rotation, the coriolis force played an important...

The peridynamic model is a framework for continuum mechanics based on the idea that pairs of particles exert forces on each other across a finite distance. The equation of motion in the peridynamic model is an integro-differential equation. In this paper, a notion of a peridynamic stress tensor derived from nonlocal interactions is defined. At any point in the body, this stress tensor is obtain...

We consider the problem of recovering an orthogonally decomposable tensor with a subset elements distorted by noise arbitrarily large magnitude. focus on particular case where each mode in decomposition is corrupted vectors components that are correlated locally, i.e., nearby components. show this deterministic completion has unusual property it can be solved polynomial time if rank sufficientl...

Implications of the Raychaudhuri equation in focusing geodesic congruences are studied framework scalar--tensor theory gravity. Specifically, we investigate Brans--Dicke and Bekenstein's scalar field theory. In both these theories, deal with a static spherically symmetric distribution spatially homogeneous isotropic cosmological model as specific examples. We find that it is possible to violate...

In this paper we aim to derive solutions for the SU($\mathcal{N}$) self-dual Yang-Mills (SDYM) equation with arbitrary $\mathcal{N}$. A set of noncommutative relations are introduced construct a matrix that can be reduced SDYM equation. It is shown these generated from two different Sylvester equations, which correspond Cauchy schemes (matrix) Kadomtsev-Petviashvili hierarchy and Ablowitz-Kaup-...

In this survey paper, a summary of results which are to be found in a series of papers, is presented. The subject of interest is focused on matrix algebraic properties of the Fisher information matrix (FIM) of stationary processes. The FIM is an ingredient of the Cramér-Rao inequality, and belongs to the basics of asymptotic estimation theory in mathematical statistics. The FIM is interconnecte...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational eld with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new eld equation generalizing the notion of Killing spinors. The solutions of this spinor eld equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einstein-Di...